Electrical gun directing system



, March 9, 1954 W W HANSEN 2,671,613

ELECTRICAL GUN DIRECTING SYSTEM Filed April 19, 1943 3 sheets-sheet 1 March 9; v19154Y w. w. HANSEN ELECTRICAL GUN JIRECTING SYSTEM 3 Sheets-Sheet 2 Filed April 19, 1945 DIFFERENCE Lim/TQ3 FIG. 5.

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March 9, 1954 W W, HANSEN 2,671,613

ELECTRICAL GUN DIRECTING SYSTEM Filed April 19, 1945 3 Sheets-Sheet 5 V;v 90\ l FIG. 6.

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|05 INVENTOR WILLIAM W HANSEN HIS ATTORNEY fire againstl surface Patented Mar. 9, 1954 zii/w13 ELECTRICAL GUN DIRECTING SYSTEM William W. Hansen, Garden City, N. Y., assigner to The Sperry Corporation, a corporation of Delaware Application April 19, 1943, Serial No. 483,679

6 Claims.

This invention relates generally to the art of gun fire control, and more particularly, to means for, and methods of, continuously controlling the firing of guns so as to effect hits against rapidly moving targets, such as airplanes. Although primarily intended as an anti-aircraft director, the apparatus of the present invention will obviously function equally Well to solve the more simple re control problems, such as directing craft, stationary targets, and

so forth.

In presently used gun directors, such as that described in U. S. Patent No. 2,065,303 entitled Apparatus for the Control of Gun Fire, issued December 22, 1936, in the names of E. W. Chafee, et al., are essentially mechanical devices. In such directors, electrical energy is utilized only to supply power for operation of the various mechanical components, such as cams, differentials, variable speed devices, and so forth, which devices mechanically accomplish all the various arithmetical and algebraic computations necessary for the solution of the fire control problem.

Some of the more important advantages of the electrical gun directing system herein disclosed over prior mechanical directors lie in its lightness, compactness, cheapness, and general simplicity. In order to attain the necessary accuracy in a mechanical director, low scale factors must be maintained throughout, and each element, therefore, must be comparatively large. As a result, the Whole director becomes a large, heavy, and unwieldy device. On the other hand, each element of the present electrical gun director is inherently small and light, and in general, the accuracy attained in each element is not a function of its size. The complete electrical gun director may, therefore, be much smaller and lighter than an equallir accurate mechanical director.

Another advantage attained in the present electrical gun director is the reduction of the shaft and gearing problem. In designing a mechanical gun director it becomes quite some -problem to actually t the various component parts together in a unitary structure of a reasonable size. This is due to the great number of shafts and gearing which must cooperate with other shafts and gearing without interfering with still other parts of the director. In the present gun director, since data is transmitted mainly in the form of electrical voltages rather than shaft displacements, it becomes possible to design each component separately with regard only to its particular function, and then simply connect the various components together with conducting (Cl. 235-6L5) leads. Besides resulting in a more compact director, such a construction also has the advantage of being easier to service.

Also, in mechanical directors considerable diiilculty is often met in insuring stable performance of the servo and follow-up devices involved. As is Well known, stable operation of such devices depends essentially on having a big difference between the time constant of the various component devices and the time constant of the complete system. Since an enormous range of time constants is readily available in the electronic equivalent of mechanical servos, this diiculty is eliminated.

Another problem encountered in the design of a mechanical director is that of backlash in the gears. Since there is no electrical equivalent to backlash, this problem is also eliminated in the present electrical director.

In presently used' mechanical directors the prediction of the future position of the target is carried out in rectangular coordinates, and is based upon the assumption that the target is flying in a straight line at a constant velocity. Since present target position data is necessarily received from the sighting system in spherical coordinates, it becomes necessary in these directors to convert these spherical coordinates into the corresponding present position rectangular coordinates to compute the future position of the target in rectangular coordinates, and then to convert these computed future position rectangular coordinates back into the corresponding future position spherical coordinates, which last data may then be employed for controlling the angular position of the gun and the fuze setting of the projectile.

In the present application there is disclosed an electrical gun director which accomplishes the prediction of the future target position in spherical coordinates directly Without lrst converting to rectangular coordinates. In the past this has been thought impractical because of the difficulty involved in obtaining the many higher order time derivatives of the incoming present position data which are necessary in order to predict in spherical coordinates. In the present application this diiculty is overcome by employing electrical differentiating and smoothing circuits, which are much more accurate and practical than mechanical differentiating circuits to obtain the necessary higher derivative data. By thus predicting in spherical coordinates, the necessary double conversion from spherical coordinates to rectangular coordinates and then back again to spherical coordinates, and the re- 3 sulting loss of accuracy involved in this double conversion are eliminated.

As previously stated, presently used fire control directors base their prediction of the future position of the target upon the assumption that the target is nying in a straight line at a constant velocity. In the present invention, the future position computed is the true future position based, not upon any assumptions at all, but upon the true mode of motion of the target as determined by the instantaneous values of the successively higher order derivatives at th'e time of firing. In this way the gun director of the present invention is capable of effectively directing gun fire against a target which is flying at an accelerating rate, or in a curved pathi or having any other mode of motion.

Another advantage accomplished by predicting in spherical coordinates is that it becomes possible to apply the present, position spherical coordinate data received from the sighting system directly to the guns as a rst approximation, and to compute in the predicting and ballistic apparatus only correction factors which may then be applied to the gun to finally position it. This avoids the necessity of carrying the major portion of the iinal gun position data all the way through the computing system, thus allowing the use of higher scale factors in the computing apparatus and resulting `in greater accuracy in the ultimate solution.

Accordingly, an object of the present invention is to provide an electrical gun directing system.

Another object of the invention is to provide a simple, cheap, compact, and accurate gun directing system.

Another object of the invention is to provide a gun director operating wholly in spherical coordinates.

Still another object is to provide electrical re control apparatus for computing the prediction corrections in spherical coordinates directly from the present position spherical coordinates of the target.

A further 'object of the invention is to provide apparatus for accurately computing the prediction corrections to be applied to a gun in order to hit -a target which iis traveling at an accel erated rate, or in va curved path, or according to any other mode of motion.

vA still further object is to provide la gun 'di'h rector wherein only correction terms 'are involved 'in thecornputing apparatus.

Other objects and Aadvantages 'will become ap'- parent in the specication taken 4in connection with the accompanying drawings wherein the lnvention 'is embodied vin lconcrete vfo'rin.

In 'the drawings,

Fig. -1 is a schematic diagram of the complete gun directing system of the present invention.

Fig. I2 is a schematic diagram of the azimuth 'component 'of the predicting circuit of Fig. 1.

Fig. 3 'a Wiring diagram of a smoothing 'and differentiating circuit which may be employed in connection with Fig. f2.

Fig. 4 is a detailed schematic diagram of the ballistic mechanism of Fig. 1.

Fig. 5 is `a schematic wiring 'diagram 0f the 1 azimuth component of the dierenceindicator of Fig. 1.

Fig. 6 is a Wiring diagramof a circuit employed for various purposes 'in the "system,

Fig. 7 -is fa representation 'of the potentiometer 4 unit employed for multiplying and for other purposes.

Fig. 8 is a wiring diagram of the sum circuit employed for algebraically adding two voltage signals.

Similar characters of reference are used in all of the above figures to indicateA corresponding parts- Arrows are used to indicate the direction of flow of information or control influences.

Referring now to Fig. 1, wherein the complete gun directing system is schematically shown, an automatic radio sighting system I is employed to obtain the azimuth angle (Ao) as a proportional rotation of output shaft 2, and the elevation angle (Eo) as a proportional rotation of output shaft 3., of the present position of the target, and to 'provide the automatic range circuit 4 with the necessary information as on output lead 5, for it to solve for and produce as a proportional rotation of shaft G., present slant range (Do).

Although the radio .sighting system may be of any suitable type adapted to accomplish this purpose, preferably a reiiected-pulse radio sighting system of the type disclosed in copending application Serial No. 441,183 for Radio Gun 'Conf trol System, Yled in the names of C. G. Holschuhet al., April '30, 1942, is employed. As de.- scr-ibed. in that application. periodic pulses of electromagnetic energy are radiated in a conical fashion about thetarget from `a suitable vreflector, schematically indicated at 7, which reiector has its radiation axis 3'? slightly oiset from its spin -axis 3-8 as shown.

Renector 'I is also employed to receive back corresponding pulses reflected .from a target lying within the irradiated conical portion of space. The phase and magnitude of the variation 'in 5intensity of the reflected pulses is then inter- .preted by suitable detecting circuits which produce output sign-al voltages proportional to the angular deviation in elevation and azimuth .of the axis ofv the cone of space irradicated (the spin axis of reflector l.) with respect to the line` of .sight of the target. I

These Voltage signals are then introduced into `sui-table servo mechanisms which reposition the spin axis Aof reflector 'l 4in such a direction as to reduce these signal voltages to zero.. this manner the spin axis is continuously maintained coincident with thev line of sight to the tar-get, thus providing .a measure of the angular position `of `the target in elevation and azimuth. The azimuth `and elevation output shafts y2 and 3 may be directly connected to the shafts which control the orientation of the spin axis so that the angular displacement fof shafts -2 and A3 will .be .respectively `propcational -to the present azimuth (Ao) and present elevation (Eo) of the target.

The automatic lrange circuit 4 receives -on lead -5 both the transmitted .pulses and the corresponding reiected pulses of electromagnetic ene ergy. As is Well-known, `the Alapse of time between a :transmitted .pulse land a corresponding .received pulse is `proportional to the distance, to the target. 'The automatic rangecircuit., which may be of the type disclosed in copen'ding application Serial No. 432,290 for 5A Pulse System, Ifiled February 25, i942 in the .name of M. Silhavy. or any `other suitable type, 'is adapted to measure this time interval 4and :provide on its output 'shaft '6 an angular displacement proportional to this time interval, and therefore proportional to 4the .slant range (De) to `the target.

yAlthough the sighting 'system 1 has been Jdescribed as an automatic radio sighting system, it is contemplated that an ordinary manually operated optical sighting device, such as a telescope, may be employed in conjunction with a conventional manually operated optical range finder in order to obtain the spherical coordinates (An, En and Do) of the present position of the target.

Referring again to Fig. l, it may be considered that an ultimate function of the computing apparatus there disclosed is to produce angular displacements of shafts 8 and 9, respectively proportional to the angle of train (A.T.) of the gun and the quadrant elevation (QE.) of the gun required for effective gun fire, and on shaft II) an angular displacement proportional to the correct projectile time of flight (tp). The operation of the computing apparatus in accomplishing the solution for angle of train will first be considered.

As shown, the present azimuth (Ao) shaft 2 is employed to actuate a permanent magnet generator II, which accordingly produces upon its output lead I2 a voltage signal corresponding in magnitude and polarity to the magnitude and `sense of the rate of change or first time derivative (o) of the present azimuth angle (Ao). This voltage signal is then introduced into the predicting circuit I3 where it is further successively differentiated in order to obtain the second and third derivatives (At) and (Ao) of the present azimuth angle. As will later be described 'in more detail, the predicting circuit I3 multiplies these successively higher derivatives by factors respectively proportional to corresponding powers of the time of flight which is received as a'proportional rotation of input shaft It from shaft IIJ, and the interconnecting shafts and gearing. The various products so obtained are then additively combined to produce on output lead I5 a voltage signal corresponding to the azimuth prediction correction (AA). This correction, which represents the change in the angular position of the target in azimuth during the projectile time of flight (tp), is then introduced into the difference indicator 25. In order to obtain the azimuth ballistic correction (t) which takes into account the variation of the projectile from a straight line course after it has left the gun, there is provided a ballistic mechanism I6. The ballistic mechanism is adapted to receive, as proportional rotations of input shafts I1, I8 and I9, data corresponding to the angle of train (A.T.), quadrant elevation (Q.E.), and time of flight (tp) from shafts 8, 9 and I0, respectively. Since the ballistic correcti'ons will be influenced both by the presently existing atmospheric conditions and also by the lmuzzle velocity of the gun, there are provided knob and graduated scale arrangements 29, 2I, 22 and 23, by proper adjustment of which data corresponding to the change in muzzle velocity (AM.V.)` from standard, the percentage change in air density (%Apa) from standard, and the velocity (Vw) and azimuthal direction (Aw) of the wind may be sent into the ballistic mechanism, The ballistic mechanism, having received these various input data, is then adapted to produce on its output lead 24 a voltage proportional to the azimuth ballistic correction as will later be'described in more detail. This voltage signal is then also introduced into the difference indicator 25.

' lThe difference indicator 25 operates in conjunction with the angle of train servo 26 and subtracting differential 21 to form a follow-up system, which system acts to angularly displace shaft 8 by an amount proportional to the present azimuth angle (Ao) appearing as a proportional displacement of shaft 2,plus the azimuth prediction correction (AA) appearing as aproportional voltage on lead I5, plus the azimuth ballistic correction (t) appearing as a proportional voltage on lead 24. Shaft 8 is thus positioned in accordance with angle of train (A.T.). Since the angle of train servo 26 drives shafts 8 and 29 equally, the angular displacement of shaft 29 also is proportional to angle of train (A.T.).

In operation the subtracting diierential 21 produces on its output shaft 28 an angular displacement equal to the diiference between the angular displacements of its two input shafts 29 and 2, and therefore proportional to angle of train minus present azimuth angle (A.T.-Au) The difference indicator 25 additively combines the azimuth prediction correction (AA) received on lead I5 and the azimuth ballistic correction received on lead 24. It then makes a comparison between this sum (AA-I-) and the difference (A.T.-Ao) received on shaft 28, and produces on its output lead 30 a voltage signal corresponding to the. difference (dA) existing in these two quantities, if any.

Since this voltage signal (dA) appearing o lead 30 is employed to control the angle of train servo 23, it will be apparent that the servo will drive shafts 8 and 29 until the voltage signal (dA) has `been reduced to zero. When this condition is met, the following relationship holds:

Ete-arranging the above equation, We obtain the following equation:

Accordingly, shafts 29 and 8 will have been angularly displaced by an amount corresponding to the present azimuth angle (A0) plus the azimuth prediction correction (AA), plus the azimuth ballistic correction and therefore by an amount corresponding to the true angle of train (A T.) required to hit the target.

Shaft 8 may then be employed to -actuate an angle of train transmitter 3|, which may be of any suitable type, such as a conventional Selsyn or Autogon, in order to transmit data corresponding to the correct angle of train (A T.) to a remote gun battery by way of output lead 32.

Similar apparatus is employed in order to compute the elevation prediction correction (AE) and the elevation ballistic correction (qts), and to produce upon shaft 9 an angular displacement proportional to the sum of present elevation angle (En) and these two corrections, that is, proportional to quadrant elevation (Q.E.). In general the apparatus employed for the solution in elevation has been given the same reference numeral as the corresponding azimuth apparatus, but has been primed. A quadrant elevation transmitter 3|', which may be identical to transmitter SI, is provided to convert the quadrant elevation signal appearing as proportional rotation of shaft 9 into corresponding electrical data appearing on lead 32. This quadrant elevation (QE.) may then also be transmitted electrically to a remote gun position.

An angular rotation of shaft I 0 proportional to the projectile time of night (tp) is produced in an identical manner, although this is a little more dilcult to understand since the corre- Referring now to Fig. 7, there is shown a potentiometer unit useful for multiplying, obtaining functions of an independent variable, and for a combination oi these two purposes. As there shown, one terminal 55 of the potentiometer 95 is connected to the ungrounded side of the input voltage signal (Vi). The other terminal 91 is grounded. The contact arm 58 of the potentiometer 95 is rotated in accordance with the shaft displacement signal (sc) from the input shaft 95. The potentiometer 95 is wound so that the resistance from the grounded terminal 91 to a particular point on the potentiometer is proportional to the Value of the function F (m) corresponding to the value of represented by that point. Conductor |00, which is electrically connected to contact arm S3, is introduced into a follower circuit which may be of the type shown in Fig. 6. The output voltage of follower -circuit 10| which appears on output lead |02 is then proportional tothe desired output signal.

It will be apparent that the voltage between :conductor |00, which is connected to the contact arm 98, and ground will be proportional to the voltage input signal (Vi) and also proportional to the function F (at) represented by the position of contact arm 00. The voltage of conductor |00 is therefore proportional to F() (Vi). This is only true, however, when the voltage across conductor |00 .is on open circuit, that is, when it is drawing no current. ln order to be able to use this signal 'without drawing current therefrom, the follower circuit |0| is provided, and the output voltage appearing on conductor |02 may be employed as the useful signal from which current supplied by the plate supply voltage of follow circuit llli, may be drawn without causing any inaccuracy. As shown and described, the potentiometer unit of Fig. '1 constitutes a function and multiplying unit wherein a voltage signal is ob-` tained on output lead 02 proportional to the product of the input signal (Vi) and a predetermined function of the input shaft displacement signal It will be apparent potentiometer 95, a voltage output signal (rc-V1) may be obtained, which is proportional to the product of the voltage input signal (V1) and the shaft displacement signal (sc). When the potentiometer unit is used in this way, it will be referred to simply as a multiplying unit. A simplified modification may also be used simply as a function unit, in which case, the potentiometer 55 would be energized from a constant source o1' direct voltage and would be wound in accordance with the desired function. In such case, an output voltage signal would be produced 'proportional to the desired function of the shaft 4displacement, input signal.

With potentiometer S5 constantly energized and linearly wound, a conversion unit is o-btained which may be employed simply to convert a shaft displacement input signal to a proportional `voltage output signal. In the drawings of Figs. 2, 4 and 5, the potentiometer unit of Fig. '1 is schematically shown, and the particular one of its four possible functions is indicated by appropriate initials marked within the unit.

Referring now to Fig. 8, wherein there is shown a circuit for obtaining the algebraic sum of two voltage input signals (V1 and V2), there are provided two electron tubes |04 and |05 which are indicated as tetrodes, although pentodes would be equally suitable. The ungrounded side vof one voltage input signal is applied to that by linearly winding the control grid of tube |04 while the ungrounded side of the other voltage input signal is applied to the control grid of tube |05. A plate supply battery |06, grounded at an intermediate point between its positive and negative terminals, supplies positive plate potential to the plates of each of the tubes through the resistor |01. The negative terminal of battery |06 is also connected to the plates of the tubes through the variable resistor |08 and resistor |09. The voltage appearing at the point H0 between resistors |08 and |09 is fed through a reversing circuit HI, which may be of the type shown in Fig. 6, and which supplies on its output lead H2 a voltage signal proportional to the sum of the two input signals (Vi-I-Vz).

The cathode of tube |04 is connected to ground through the biasing resistor I I3 and inverse feed back resistor H4, and the cathode of tube |05 is.

connected to ground through respectively identical biasing and inverse feed back resistors ||5 and H0. The negative terminal of the battery is connected to a point H1 midway between resistors I I3 and H4 through the variable resistor H8. A similar connection is made from the negative terminal of the battery through the variable resistor IIB to a point |20 midway between resistors H5 and HS. The screen grids o f both tubes may be connected to the positive terminal of the battery, as shown. With both tubes |04 and |05 operating at their quiescent conditions, that is, with both input signals at zero potential, the variable resistors |08, H8 and H9 are adjusted so that the points H0, ||1 and |20, respectively, are at zero potential.

In operation, when a positive voltage input signal (V1) is received on the control grid of tube |04, the resulting increase in current flow through resistor |01 lowers the potential applied to the plates of both tubes. Since both tubes are tetrodes, this reduced plate voltage will have substantially no effect on the flow of current through tube |05. The reduction of theplate potential, however, will cause the potential of point H0 to I become negative by an amount corresponding to Since the amount of current flowing through resistor |01 is the sum of the currents owing through each of the tubes, and since the current through each of the tubes is dependent only on the input voltage signal applied to its control grid and is independent of the current flow through the other tube, it will be apparent that the potential at point I I0 will be proportional in -magnitude to the algebraic sum (Vi-I-Vz) of the received input signals, but opposite in polarity. The polarity of this resultant potential is reversed in reversing circuit I so that the volt-age signal appearing on output lead H2 corresponds both in polarity and magnitude to the algebraic sum (Vi-i-Vz) of the received input signals.

Inverse feed back for tube |04 is provided by resistors H3 and H4 and for tube |05 by re- Asistors I5 and I6. As the current through tube |04 increases or decreases as the resultant of the receipt of a. voltage signal upon its control grid, the resulting change in cathode potential caused 11 by thel change in current now through resistors I I3 and I [4 will tend to oppose the effect of the received signal voltage applied to the grid. An increase or decrease in current ow through resistors H5 and. H 5 acts ina similarfwayin opposition to the received voltage signal` (V2) causing the increase or decrease.. There is thus provided the required inverse feed back required for effecting an accurate summation of the received signals.

It willbe appreciated that the vsum circuitY characterized by lig.V 8 is not limited to obtaining the algebraic sum of only two voltage input ,signals, but that any number of voltage input signals could be algebraically added. For each additional input signalv another tetrode would be required connected in the circuit identically with tubes |54 and |85 so that its plate current also would 'flow through the common plate resistor M1.

Returning ,now to a consideration ofthe prediction problem, that is, the manner in which the predicting circuit I3 solves` for the `prediction corrections (AA, AE and' AD) in azimuth, elevation, and slant range, respectively. It may be said that no matter in what manner the target may be moving, each of its coordinates will instantaeously have some specic law of motion which defines the value of that coordinate as a function of time, and which may be expressed for the azimuth coordinate, for instance, by the following formula:

wherein zero time istaken as the time Iat which we are attempting to perform thel predicting, that is'L when A=Ao, and the asare unknown Coenicients. If then it is desired to determine the angular orientation oi" the target in azimuth at a time (tp) later, We may employ a Tay-lor series as follows:

A().=A+ (z;)+

im 'fr Tfr) 'une ML 11, 2H +"we "L i' i The lazimuth prediction correction (AA) is then equal to the sum of all the terms in the above expression subsequent to the rst, or Aa term.

ndot Aeon 2 3 unan-2e @el i.

This expression is employed in predicting, circuit i3 to obtain ay voltage signal proportional to' the azimuth prediction. correction (AA).A

As. show-n Fig 2', the; voltage' from permanent magnet generator il appearing on input lead 122 and corresponding to the first derivative (u) of the azimuth angle (Au), is introduced into a sum circuit il which may be ofthe type disclosed in Fig. 8; asl on lead 59, and also into a smoothing and differentiating circuit 42', as on leadl 4D. As will more fully-be explained hereinafter, smoothing and' di'iierentiating circuit 42 is adaptedto further successively dilerentiate the inputY first deriva-tivel data, thereby producing on output leads 53 Eri voltage signals corresponding to the second (u and third (Ac) derivatives of the azimuth angle.

Three potentiometer multiplying units 45, 46 and 4'?, are provided, the contact armof each of which is actuated in accordance with a required value off' time of night (tp)- received asa propertional rotation. of input shaft M. Potentiometer unit ll'fis` en ergized in accordance with the third derivative (Au) and its contact arm is rotated proportionally to one-third time of flight (tp),v by reduction gearing 41', to produce uponnits output lead i8 a` voltage proportional to l/aAotp. This voltage is then added in the sum circuit 49,110 the voltage appearing on lead 43 to produce upon lead. 5t' a voltage ,proportional to o+ 1/3Aotp.

The voltage signal thus appearing on. lead 50 is then multiplied in potentiometer` unit 46 by one-half the time of flight, to produce upon lead 5ly a voltage proportional to 1/2otp+%A0(tp)". This voltage is then added to the voltage received on input lead l 2, and the sum is again multiplied by the time of flight in potentiometer multiplying unit 55 to produce a voltage on output lead l5 lproportional to otp+1utp2+ l/sAotpa. This voltage may then be taken as proportional to the azimuth prediction correction (AA) `as derived from Taylors series since mathematical investigati'on of the anti-aircraft problem discloses that for the types of target courses most likely to be encountered under combat conditions the rst three terms of this series provide sucient data to obtain the degree of accuracy required in the final solution.

In Fig. 3 there is shown apparatus which may be employed in smoothing and differentiating circuit d2 to accomplish the function oi that circuit. As there shown, the voltage received on input lead 40' corresponding to the rst derivative (A0) of present azimuth angle (An) is placed across a series circuit consisting of the condenser 55 and resistor 51. Since the charging current owing into condenser 56 will be proportional to the time rate of change of the voltage appearing on lead 4D, the current through resistor 51, consisting only of this changing current, will be proportional to thetimerate of change of the first derivative (.fr) or, in other words', proportional tothe second derivative (o') The voltage across resistor 51, corresponding therefore to the second derivative (o) of the present azimuth angle, is fed to the grid of an electron tube 58. The cathode of tube 58 is connected to ground through the resistor 59 and the parallel circuit consisting of the condenser 60 and resistor 6l. The plate supply battery 62 has a point intermediate to its positive and negative terminals grounded. The plate of tube 58 is connected directly to the positive side of battery B2. The negative side of' battery 62 is connected through the variable resistor 63 to a point intermediate resistors 59 and 6l. It will be evident that electron tube 58 and its associated circuit elements constitute a follower circuit of the type shown in Fig.. 6, except for the addition of the condenser 6D across resistor 6 l.

As is Well known, the Apresent azimuth data received from the radio sighting system I and appearing as a proportional rotation of shaft 2, Will always have some erratic perturbations superimposed upon the true value represented thereby. This is caused by the impossibility of obtaining perfect servo systems in the radio sighting system l for accurately following the target, by backlash in the gearing, and so forth. 'I'hese erratic variations appearing on shaft 2 will be reflected as correspondingv variations in the rst derivative voltage signal appearing on leads l2 and 40. These variations in the first' derivative data. in turnl will be reflected into the' voltage signal appearing across resistor 5T and represent'- 13 ing the second derivative (o) of the azimuth angle. The purpose of condenser 60 is to operate in conjunction with resistor 6| to form a simple smoothing circuit in order to average out the resulting false variations in the second derivative data. Accordingly, there is produced an output lead 43 a voltage signal (ws proportional to a smoothed measure of the second derivative voltage signal appearing across resistor 51.

In order to obtain a voltage on lead 44 proportional to the third derivative (Ao) of the present azimuth angle, the voltage appearing on lead 43, representing the second derivative (u), may be re-differentiated and re-smoothed by introducing it into apparatus identical with that just described for obtaining the second derivative. If desired, more rened circuits for differentiating and smoothing may be employed. Also, in obtaining the azimuth prediction correction (AA), only the first three derivatives have been utilized, It will be apparent that by applying the principles 4of operation of the invention which have been described, it is possible to carry as many terms of the Taylor series as is desired.

Since the elevation prediction correction (AE) and the slant range prediction correction (AD) may be obtained in the same manner as described for obtaining the azimuth prediction correction (AA), a further description of the predicting apparatus is not necessary.

In Fig-4 there is shown the ballistic mechanism I6 of Fig. 1, the purpose of which is to receive time of flight (tp), quadrant elevation (Q. E.) and angle of train (A. T.), represented by the displacements of shafts I0, 9 and 8, respectively, and to produce from these input signals and from other input signals corresponding to the change in muzzle velocity (A M. V.), percentage change in air velocity (%Apa), and the velocity and azimuthal direction of the wind (Vw and Aw), the azimuth, elevation and slant range ballistic corrections ps and p) as proportional voltages or output leads 24, 24 and 24, respectively.

Angle of train (A. T.) received on input shaft |1 is introduced into a Wind resolver |22. The purpose of the wind resolver, which also receives the velocity and azimuthal direction of the wind from knobs 22 and 23, respectively, is to produce on its output shafts |23 and |24 angular displacements respectively proportional to the rearwind velocity (Wr) and the cross-wind velocity (We) The wind resolver' may consist of a differential in which the dierence between the azimuthal wind direction (Aw) and the angle of train (A. T.) is obtained. This difference may be introduced into a disc and slide mechanism of the type which is employed in U. S. Patent No.

2,065,303, entitled Apparatus for the Control of Gun Fire and issued December 22, 1936 in the names of E. W. Chafee et al. for the purpose of resolving the coordinates (Rn) and (Ao) of the present position of the target in the horizontal plane into the corresponding rectilinear coordinates (xo) and (yo). The disc and slide mechanism is employed in a similar manner in the present device to compute the required components of wind velocity (Wr and We) along and across the line of fire, from the velocity of the wind and its angular direction with respect to the line of re. Such a wind resolver, as has herein been described, is shown and described more completely in the aforementioned copending application Serial No. 470,686, wherein it is used for an identical purpose.

'14 The conversion units |26 and |25, respectively, actuated from shafts |24 and |23, produce on their output leads |28 and |21, voltage signals proportional to the cross-wind velocity (We) and the rear-Wind velocity (Wr), respectively. The conversion unit |29, actuated in accordance with the percentage change in air density (%Apa) from shaft |30 and knob 2|, produces a proportional voltage on its output lead |3|. Similarly, the conversion unit |32, which is actuated in accordance with the change in muzzle velocity (A M. V.) from knob 2D and shaft |33, produces on its output lead |34 a voltage proportional to change in muzzle velocity.

The desired azimuth ballistic correction is calculated in the ballistic mechanism in accordance with the formula:

In this formula and the following formulae, subscripts f and g are used to indicate different functions of time of flight and quadrant elevation, respectively. These functions are obtained from data given in firing tables which have been empirically compiled.

In order to compute the azimuth ballistic correction in accordance with the above formula, the function unit |35 and the function and multiplying unit |36 are actuated in accordance with time of flight (tp) from input shaft I9, and the function and multiplying units |31 and |38 are actuated in accordance with quadrant elevation (Q. E.) from input shaft |8. The predetermined function of time of flight ,f1(tp) produced by the function unit |35 is multiplied by the proper predetermined function of quadrant elevation g1 (Q. E.) in the function and multiplying unit |31 so that there is produced on lead |39 ayvoltage proportional to the rst quantity of the equation for the azimuth ballistic correction In a similar manner, the cross-wind velocity (Wc) is successively multiplied by the proper function f2(tp) of time of flight and the proper function gz (Q. E.) of quadrant elevation in the function and multiplying units |33 and |38, respectively. This product, which is equal to the second quantity in the equation for the azimuth ballistic correction is produced as a proportional voltage signal on lead |4. The sum circuit 4| operates to add the input voltages received on leads |39 and |40 and to produce Ion its output lead 24 4a voltage proportionalv to the azimuth ballistic correction in accordance with the above formula.

The elevation ballistic correction or super.- elevation (os) is computed in accordance with the following formula:

wherein the first quantity is the elevation ballistic correction existing under standard con'ditions and the next succeeding quantities take into consideration the actual conditions of rearwind, air density, and muzzle velocity existing at the time of the solution.

In order to solve for the elevation ballistic correction (cs) according to the above formula, the function unit |42 and the function and multiplying units |43, |44 and |45 are all actuated in accordance with the time of flight (tp) from shaft I9, and the function and multiplying units |46, |41, |48 and |49 are actuated'in accordance with quadrant elevation (Q. E.) from shaftl. The function and multiplying units |43, |44 'and `|45 1%5 are respectively; cnergizediin; accordance with' the rearfwindrvelocity (We) percentage change.. in air density (%Aps) and the change muzzle veloc- `ity- (AM. Vx).` from leadsr 1.2.21. |31; and L34, respectively.

In, accordance with the theory of operationl of the'function; and multiplyingzunits.. which by now should: bei well understood; there are. produced as. proportional voltagesy on. leads |50, |51, |52 and |53, measures ofl each of. the-.four quantities comprising the lelevation ballistic correction (es) The. sum.. circuit |151 operates. to combine these fourquantities andtoproducezon lead24! voltage proportional to the elevation ballistic correction (ci) in.` accordancewith the above set out-formula.

The slant range ballistic correction (pl is; similarly computed in accordance with the following formula:

wherein theV first two quantities are suiiicientv to compute the slantrange ballistic correction under .normal conditions and the last three take care of existing variations from the.V normal'. conditions.

Asshown, the function units |55 and |56, and theftunction and multiplying units |51, |58 and m9,. are actuated from the time of flight shaft. I9, and the function and multiplying units |60, ISI, |62 and |63 are actuated in accordance with quadrant elevation from shaft I8. Thev function and multiplying units |51.. |156 and |59 are respectively energized from leads |21., ttl and |34 in accordance Withthe rear Wind velocity and; the

variations in an; density-and muzzle velocity from standard conditions', respectively; The various function and function. and multiplying units opverate'toJ produce on. leads` |643, |565., |66, |61 and |68. voltages pronortionalV to the various quantities comprising the slant. range ballistic correction. fpl.. The Sumoirouit |619: performs the re- Vquired algebraic addition of these various quan titiesv in: accordance withl thel above formula. There is-accordingly produced on output lead 24." a voltage proportional to the slant range ballistic correction; (fp).

Referring new to Fig. 5. wherein the azimuth component of the dii-.Terence .indicator 2.5' of. Fig. l is schematically shown, a conversion potentiometerunit 64. is provided tov convert, the. angular displacement of input shatt- 28; into a. voltage on output `lead? 65 corresponding in magnitude. but having an opposite polarity. It will be recalled that the angular displacement of Shaft 2,8; is pro- DOrtional to the difference between theangle of vtir-air; (Ag. i-2), appearing as a. proportional rotation of shaft 29, and the present, azimuth angle (Ao), appearing as proportionalrotation of, shaft 2. The voltagesi'gnal appearing on lead 65, therefore, corresponds to the quantity -(A.T.-A0). This-:voltageis introduced into a. sum circuit 66. Alsointroduced into sum circuit 66, as on leads iid and 24, respectively, are voltage signals corresponding to the azimuth prediction correction (fd/Ai and the. azimuth ballistic correction (t). The sum of all these input voltageY signals is thus produced on. output lead 30. Accordingly, the voltage appearing von output lead 30 is the required signal voltage (dA) for actuating the angle of tra-in servo 2t as expressed by the following relationship:

previmislxzy stated, shafts 8. and 29- wilt: .continuetoabe driven` by servo 2.6. voltage signal (dit) nas been reduced. to zero. at which. time shaft 8 will have beeny angularly displaced an amount proportional to the angle of train (iAJT.) at which the gun must be positioned for effective gun lire. The elevation and slant range components. of` difference indicator 2,5 obtain the elevation and slant range voltage signals (dE and dD) in an identical manner.

It Will be apparent that electrical calculating devices for performingv the various operations. ac'- complished byA the devices shown in Figs. 6 through 84 could be designed to operate on: alte!- nating current voltage signals asv Well: as dileet current voltage signals. desired, suchdevices could then be incorporated in the gun directing system described, withonly slight modiiication of the system, thus providing aguil. directingsystem operating on alternating current throughout. 1t is. therefore, not intended that the. present nvention be lilnitedv to the use of direct current voltage signals.v

since. many changes could be madein the above construction many apparently Widely different embodiments of this invention could be made without departing from the scope thereof, itis intended that ail matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrativeI and not in a limiting sense.

What. is claimed is;

1. A predictor comprising. .in combination.` an input. terminal adaptedto received quantity proportional to the first derivative of a variable, a smoothing and di1Terentiating circuitfor converting the quantity applied to the input terminal: vinto second and third derivatives respectively.. a plurality of potentiometers each having a siidable tap.v and a common drivingl means adePtedto be rota-ted in proportion to an. independent variable, connections for applying the third derivative quantity to the rst potentiometer. a summing circuit with input connections. from a second derivative terminal of the smoothing and differentiatingv circuit and` from the tap. of the first potentiometer, an output connection` from' said summing circuit to the second potentiometer, a second summing circuit with input connections from. the tap of the second potentiometer and from the input terminal of the apparatus', and output connection to the third potentiometer, the tap of thethird potentiometer having an. outputV terminall at which the predicted value appears.

2. AA prediction circuit for a gunfire director comprising, in combination, an input terminal to which a voltage may be applied proportional to the rstderivatve of one of the independent variables` of a prediction problem representing one of the coordinates of the target, adiflerentiating; circuit having an input from said terminal, a first output terminal at which aV second derivative voltage appears, and a second output terminal at which a third derivative voltage appears, three potentiometers. with a driving shaft adapted to move in proportion totime of Hight of a. projectile, each of said potentiomet'ers cornpiising a pair of relatively movable elements, one of which comprises an impedance winding. and the other of which comprises a sliding tap. .first and second summing circuits,v an input connection from the third derivative terminal to the winding of the rst potentiometer, input. connections to the. first summing circuit from the second. derivetiveterminal and; the tap of: the first potentiometer, an outputelliieiifln from the first summing circuit to the winding of the second potentiometer, input connections from the apparatus input terminal and the tap of the second potentiometer to the second summing circuit, an output from the second summing circuit to the winding of the third potentiometer, and an output connection from the tap of the third potentiometer on which a Voltage representing predicted value appears.

3. A predicting circuit for a gunfire director` comprising, in combination, an input terminal to which a function of one of the coordinates of the moving target may be applied, a difierentiating circuit having an input connection from said terminal, and a plurality of output terminals at which appear quantities representing` successively higher derivatives of the quantity applied to the input terminal, a plurality of summing circuits equal to the number of output terminals of the differentiating circuit, a plurality of potentiometers, one greater than the number of summing circuits, each of the potentiometers except the last having one of said summing circuits associated therewith, each of said summing circuits having one input from one of the said terminals and a second input from one of the potentiometers and having an output to a succeeding potentiometer, the rst potentiometer having an input from the highest derivative terminal of the differentiating circuit, whereby the last potentiometer has an output representing the Taylor series in which the number of terms is equal to the number of potentiometers employed, and terms of the Taylor series are power functions of projectile time of flight and derivative functions of the coordinate of the target.

4. Apparatus for computing a Taylor series in terms of a rst and second variable, comprising means for diierentiating a rst variable, a terminal at which a quantity proportional to the first derivative appears, means for successively differentiating, having terminals at which successively higher derivatives appear, a plurality of potentiometers equal in number to the number of derivative terminals, each potentiometer comprising a pair of relatively movable elements, one of which consists of a winding and the other of which consists of a slidable tap, means for producing relative motion of said potentiometer elements in proportion to the second of two variables in terms of which the Taylor series is to be produced, and a plurality of summing circuits one less in number than the number of potentiometers, the iirst of said potentiometers having an input to its winding from the highest derivative terminal, all of the potentiometers except the last having a summing circuit associated therewith, each of said summing circuits having a pair of inputs, one from the tap of the potentiometer with which it is associated, and a second from the derivative terminal, one lower in order than the derivative terminal to which the summing circuit of the preceding potentiometer is connected, and each summing circuit having an output terminal connected to the winding of the next succeeding potentiometer, whereby a quantity proportional to 18 the sum of the Taylor series terms appears upon the tap of the last potentiometer.

5. An electrical predicting circuit comprising, in combination, a differentiating device having an input terminal to which a derivative quantity is adapted to be applied, output terminals to which successively higher derivatives of an input quantity are supplied by the differentiating circuit, a plurality of potentiometers having relatively movable members comprising windings and taps respectively, and a common driving means therefor movable in proportion to the second quantity, a plurality of summing circuits one less in number than the number of potentiometers, each summing circuit having an output connection to one of the potentiometers, and a pair of input connections, one from one of the potentiometer taps and the other from one of the said derivative terminals, whereby a quantity proportional to the predicted value appears upon the tap of the remaining potentiometer.

6. Apparatus for computing a series of terms representing a function oi' first and second variables, said apparatus comprising an input terminal, means for diiferentiating an input quantity to produce successively higher derivatives of the first variable with terminals at which such derivative quantities appear, a plurality of potentiometers and summing circuit means, each of said potentiometers comprising a pair of relatively movable elements, one of which is a winding and the other of which is a sliding tap and having a common driving connection for producing relative movement of the elements of the potentiometers proportionally to the second variable, said summing circuit means having dual input connections from successively higher derivative terminals and successive potentiometer taps respectively, and the last of said potentiometer taps having an output circuit at which the computed value appears.

WILLIAM W. HANSEN.

References Cited in the le of this patent UNITED STATES PATENTS Number Name Date Re. 16,734 Schneider Sept. 6, 1927 865,247 Hubbard Sept. 3, 1907 1,322,153 Wilson et al. Nov. 18, 1919 1,345,697 Routin July 6, 1920 1,345,703 Routin July 6, 1920 1,472,590 Ford Oct. 30, 1923 1,778,201 Rutherford Oct. 14, 1930 1,939,675 Ely Dec. 19, 1933 2,105,985 Papello Jan. 18, 1938 2,206,875 Chafee et al July 9, 1940 2,231,929 Lyman Feb. 18, 1941 2,235,826 Chafee Mar. 25, 1941 2,244,369 Martin June 3, 1941 2,251,155 Neuhaus July 29, 1941 2,251,973 Beale Aug. 12, 1941 2,256,787 Lazar Sept. 23, 1941 2,324,797 Norton July 20, 1943 2,366,658 Svoboda Jan. 2, 1945 FOREIGN PATENTS Number Country Date 167,191 Great Britain May 21, 1919 

